Combine the butter and basil in a food processor and process until smooth, season with salt and pepper, to taste, and pulse a few more times. Scrape into a small bowl.
Put a large saute pan on the grill over low heat and add the basil butter. When the butter is hot add the corn kernels and saute for 3 to 4 minutes. Transfer to a serving bowl and garnish with torn basil leaves and scallions.